Logic Seminar
Gabriel Conant
UIC
Stable functions and Følner's Theorem
Abstract: In 1954, Følner proved the following discrete analogue of Steinhaus's Theorem: If $A$ is a set of positive upper Banach density in an abelian group $G$, then $A-A$ almost (i.e., modulo zero Banach density) contains a neighborhood of the identity in the Bohr topology on $G$. An analogous result for countable discrete amenable groups was proved by Beiglbock, Bergelson, and Fish in 2010 using ergodic theory. In this talk, I will present a proof of this result which is valid for arbitrary discrete amenable groups and is directly inspired by fundamental ideas and facts from local stability theory in continuous logic. Familiarity with continuous logic (or any logic) will not be necessary.
Tuesday November 26, 2024 at 4:00 PM in 636 SEO